Question

A gambler is deciding whether or not to take a bet. She must pay $40 to take the bet, but if she wins, she will profit $225. The probability that she wins the bet is 1/4 .

a) What is the player's expected value in this situation?
b) If the gambler made this exact bet many times, should she expect to win money or lose money over the long run?

Answer 1

The classification of that same given problem is outlined in the following portion on the clarification.

Explanation:

⇒
`E[x]=\Sigma_(x=0)^(x) \ x \ f(x)`

On putting the values, we get

⇒
`=0* (3)/(4)+225* (1)/(4) -40* 1`

⇒
`=(225)/(4)-40`

On taking L.C.M, we get

⇒
`=(225-160)/(4)`

⇒
`=(65)/(4)`

⇒
`=16.25`

1...

Whether she wins she would receive $225 with even a 1/4 chance, then she will lose and maybe get $0 with such a 3/4 chance although if she takes a gamble anyway though she will either have to compensate $40 wp 1.

2...

She seems to want the capital to benefit or win.